题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052607-55357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052607-10674.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052607-25272.png)
(2)如果函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052607-69411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052607-12262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052608-13783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052608-40651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052608-42599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052608-21606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052608-72326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052609-18346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052608-40651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052608-42599.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052609-10438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052607-25272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052609-31188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052609-93397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052610-62882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052610-23824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052610-52791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052610-79802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052611-18283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052611-92844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052611-25421.png)
(2)作差构造新函数证明.
解析
试题分析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052611-72695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052611-44663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052607-10674.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052612-40377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052612-16911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052612-29247.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052609-10438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052612-23040.png)
在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052609-31188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052609-93397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052612-48898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052610-62882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052613-69206.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052607-25272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052609-31188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052609-93397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052610-62882.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052610-23824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052613-91096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052607-25272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052610-52791.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052610-79802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052613-68262.png)
在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052611-18283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052611-92844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052612-48898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052611-25421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052613-69206.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052607-25272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052611-18283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052611-92844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052611-25421.png)
(2)令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052613-24563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052613-91770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052614-83535.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052614-83975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052612-16911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052614-94033.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052608-72326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052614-87319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052615-24626.png)
从而在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052609-18346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052615-36633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052615-98926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052609-18346.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052615-86953.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052608-72326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052615-44980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052616-99364.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052616-18141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052616-38377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052607-12262.png)
所以在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052609-18346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052608-40651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052608-42599.png)
点评:本题主要以新定义为载体,综合考查了函数的单调性、函数的最值方程的根的情况、二次函数的最值的求解,考查了利用已学知识解决新问题的能力,考查了推理运算的能力,本题综合性较强.
核心考点
试题【已知函数,其中常数.(1)求的单调区间;(2)如果函数在公共定义域D上,满足,那么就称 为与的“和谐函数”.设,求证:当时,在区间上,函数与的“和谐函数”有无穷】;主要考察你对常见函数的导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052551-25800.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052551-82471.png)
(1)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052551-25723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052552-77178.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052552-35861.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052552-65810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052552-42233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052552-35861.png)
(3)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052553-78479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052530-52200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052530-88090.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052531-23918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052531-52722.png)
(2)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052531-52722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052531-60519.png)
(3)试证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052531-92051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052525-72351.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052525-26954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052526-62756.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052514-53151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052514-54888.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052514-98702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052514-47256.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052514-57299.png)
(Ⅱ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052515-64644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052515-59514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052515-12825.png)
值.
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052503-19647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052504-81138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018052504-66500.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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